That is theory.
But the electrodes are part of a closed circuit.......So, ill gues that changes things?
Its interesting you mention that you mention that...these wer old expieriments and i dont have the picture of the coils core split with the clear rubber tube attatching them together via....yep you guessed it ...with a spark gap.
Can a magnetic field increase the current of a spark gap? .....i think so.
Can an electromagnetic field be used to vary the current of a spark gap? .....i think so.
Is the current simpler to feedback to drive the system?... i think so.
So its a matter of magnetic field requirements matching a required current flow driving a compound resonate system to do work.Work being the movement of created charged ions,pairing of electrons in a resonate condition to form a highly reactive gas.....ohhhh boy.